GibbsACOV (version 1.1)

acovamcmc: Gibbs sampler for one-way mixed-effects ANOVA and ANCOVA models.

Description

Gibbs sampler for one-way mixed-effects ANOVA and ANCOVA models using flat priors.

Usage

acovamcmc(Y, trt, X, nochn, numIter, initval, credint = 0.95, Rthresh = 1.1)

Arguments

Y

Vector of reponses of n subjects

trt

Vector of categorical factor levels for n subjects

X

Design matrix with dimension (n x p) where p is the number of continuous predictors (for ANOVA, p = 1 to include grand mean)

nochn

Number of chains to test convergence of the Gibbs sampler

numIter

Number of iterations in the Gibbs sampler

initval

Matrix of initial values for Gibbs sampler with dimension (nochn, (p + nlevels(trt) + 2))

credint

Coverage probability for parameter credible intervals

Rthresh

Gelman-Rubin diagnostic for test of convergence

Value

S3 acovamcmc object; a list consisting of

beta

values of regression coefficients for each iteration

sig2a

values of mixed-effect variance for each iteration

sig2e

values of error variance for each iteration

Credible_Interval

lower bound, point estimate, and upper bound for parameters

Credible_Interval_Coverage

coverage percentage for credible intervals

Convergence_Diag

status of Gibbs sampler convergence using threshold set for Gelman and Rubin's diagnostic

Gelman_Rubin_Threshold

threshold set for Gelman and Rubin's diagnostic

Iterations

number of iterations of Gibbs sampler

Run_Time

total elapsed seconds

References

Gelman, A and Rubin, DB (1992) Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457-511.

Examples

## Not run: 
# # ANCOVA with 2 continuous predictors and 5 factor levels
#   data(corn)
#   init1 <- c(rep(0,7), 1, 1)
#   init2 <- c(rnorm(7), rgamma(2,2,1))
#   init3 <- c(rnorm(7), rgamma(2,2,1))
#   init4 <- c(rnorm(7), rgamma(2,2,1))
#   initval <- rbind(init1, init2, init3, init4)
#   acovamcmc(corn$yield, corn$variety, cbind((corn$nitrogen)^2, corn$nitrogen), 4, 10000 , initval)
# # ANOVA with grand mean parameterization and 12 factor levels
#   data(csection)
#   init1 <- c(rep(0,13), 1, 1)
#   init2 <- c(rnorm(13), rgamma(2,2,1))
#   init3 <- c(rnorm(13), rgamma(2,2,1))
#   init4 <- c(rnorm(13), rgamma(2,2,1))
#   initval <- rbind(init1, init2, init3, init4)
#   Y = log(csection$rate / (1-csection$rate))
#   acovamcmc(Y, factor(csection$hospital), matrix(1,length(csection$hospital),1), 4, 10000, initval)
# ## End(Not run)